This article explains how to send a reply and archive the email in Gmail with one click by adding a 'Save & Archive' button to the Gmail reply screen.

Keyboard shortcuts are a blessing for saving time, but sometimes they’re unnecessary. Take the e shortcut in Gmail, for example. When you’re done with an email but don’t want to throw it away, just click e to archive it.

This works, but you can deliver the response and archive the conversation with one click, which would make your Gmail experience even more effective. To enable the Send & Archive button in Gmail:

Click the Settings gear in the top right corner of your Gmail screen.